Common unfoldings of polyominoes and polycubes

Greg Aloupis, Prosenjit K. Bose, Sébastien Collette, Erik D. Demaine, Martin L. Demaine, Karim Douïeb, Vida Dujmović, John Iacono, Stefan Langerman, Pat Morin

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    This paper studies common unfoldings of various classes of polycubes, as well as a new type of unfolding of polyominoes. Previously, Knuth and Miller found a common unfolding of all tree-like tetracubes. By contrast, we show here that all 23 tree-like pentacubes have no such common unfolding, although 22 of them have a common unfolding. On the positive side, we show that there is an unfolding common to all "non-spiraling" k-ominoes, a result that extends to planar non-spiraling k-cubes.

    Original languageEnglish (US)
    Title of host publicationComputational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Revised Selected Papers
    Pages44-54
    Number of pages11
    Volume7033 LNCS
    DOIs
    StatePublished - 2011
    Event9th International Conference on Computational Geometry, Graphs and Applications, CGGA 2010 - Dalian, China
    Duration: Nov 3 2010Nov 6 2010

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume7033 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other9th International Conference on Computational Geometry, Graphs and Applications, CGGA 2010
    CountryChina
    CityDalian
    Period11/3/1011/6/10

    Fingerprint

    Polyominoes
    Unfolding
    Regular hexahedron

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Aloupis, G., Bose, P. K., Collette, S., Demaine, E. D., Demaine, M. L., Douïeb, K., ... Morin, P. (2011). Common unfoldings of polyominoes and polycubes. In Computational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Revised Selected Papers (Vol. 7033 LNCS, pp. 44-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7033 LNCS). https://doi.org/10.1007/978-3-642-24983-9_5

    Common unfoldings of polyominoes and polycubes. / Aloupis, Greg; Bose, Prosenjit K.; Collette, Sébastien; Demaine, Erik D.; Demaine, Martin L.; Douïeb, Karim; Dujmović, Vida; Iacono, John; Langerman, Stefan; Morin, Pat.

    Computational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Revised Selected Papers. Vol. 7033 LNCS 2011. p. 44-54 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7033 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Aloupis, G, Bose, PK, Collette, S, Demaine, ED, Demaine, ML, Douïeb, K, Dujmović, V, Iacono, J, Langerman, S & Morin, P 2011, Common unfoldings of polyominoes and polycubes. in Computational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Revised Selected Papers. vol. 7033 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7033 LNCS, pp. 44-54, 9th International Conference on Computational Geometry, Graphs and Applications, CGGA 2010, Dalian, China, 11/3/10. https://doi.org/10.1007/978-3-642-24983-9_5
    Aloupis G, Bose PK, Collette S, Demaine ED, Demaine ML, Douïeb K et al. Common unfoldings of polyominoes and polycubes. In Computational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Revised Selected Papers. Vol. 7033 LNCS. 2011. p. 44-54. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-24983-9_5
    Aloupis, Greg ; Bose, Prosenjit K. ; Collette, Sébastien ; Demaine, Erik D. ; Demaine, Martin L. ; Douïeb, Karim ; Dujmović, Vida ; Iacono, John ; Langerman, Stefan ; Morin, Pat. / Common unfoldings of polyominoes and polycubes. Computational Geometry, Graphs and Applications - 9th International Conference, CGGA 2010, Revised Selected Papers. Vol. 7033 LNCS 2011. pp. 44-54 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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